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微分几何

发布日期:2013-01-10     作者: admin     浏览数:    分享到:

科研团队简介

研究方向:微分几何
 
研究对象及发展前景

主要研究整体与局部微分几何中的各种问题。涉及子流形几何、几何分析、黎曼泛函、曲率与拓扑等领域。近期主要的研究成果是球面中Moebius等参超曲面的分类和仿射微分几何中局部非退化超曲面的分类。

团队成员
胡泽军,博士,教授

翟书杰,硕士,讲师职称。

团队成员承担的主要科研项目

2007-2009年主持国家自然科学基金(现目编号10671181)、2000-2003年主持河南省杰出青年科学基金、2004-2006年主持教育部留学回国人员科研启动基金、1999-2001年主持河南省自然科学基金(项目编号994050200)。2000-2002年参加国家自然科学基金(项目编号19971060)。

团队成员发表的主要科研论文
1.Hu Zejun, Li Haizhong, Simon Udo, Vrancken Luc,           On locally strongly convex affine hypersurfaces with parallel cubic form, Part I, Differential Geometry and Its Applications, 27, 188–205, 2009.
 
2.Hu Zejun, Tian Xiaoli,           On Moebius form and Moebius isoparametric hypersurfaces, Acta Mathematica Sinica, English Series, 25 (12), 2077–2092, 2009.
 
3.Hu Zejun, Zhai Shujie,           Classification of Moebius isoparametric hypersurfaces in , Tohoku Mathematical Journal, 60, 499–526, 2008.
 
4.Feng Pinghua, Hu Zejun,           An -estimate for surfaces of constant mean curvature in , Archiv der Mathematik, 91, 461–470, 2008.
 
5.Hu Zejun, Yang Fan,           A new variational characterization of four-dimensional manifolds with constant scalar curvature, Results in Mathematics, 52, 315-321, 2008.
 
6.Hu Zejun, Li Haizhong and Vrancken Luc,           Characterisations of the Calabi product of hyperbolic affine hyperspheres, Results in Mathematics, 52, 299-314, 2008.
                                                           
7.Hu Zejun, Li Haizhong and Simon Udo,           Schouten curvature functions on locally conformally flat Riemannian manifolds,Journal of Geometry, 88, 75-100, 2008.
 
8.Hu Zejun,Scherfner Mike and Zhai Shujie:           On spacelike hypersurfaces with constant scalar curvature in the de Sitter space, Differential Geometry and Its Applications, 25, 594–611, 2007.
 
9.Hu Zejun and Li Deying,           Moebius isoparametric hypersurfaces with three principal curvatures, Pacific Journal of Mathematics, 232 (2), 289-311, 2007.
 
10.Hu Zejun, Li Haizhong and Wang Changping,           Classification of Moebius Isoparametric Hypersurfaces in , Monatshefte fuer Mathematik, 151, 201–222, 2007.
 
11.Hu Zejun and Zhai Shujie:          Hypersurfaces of the hyperbolic space with constant scalar curvature,Results in Mathematics, 48, 65-88, 2005.
 
12.Hu Zejun and Zhao Guosong:           Some remarks on the Kozlowski-Simon conjecture for affine ovaloids, Banach Center Publications, 69, 189-193, 2005.
 
13.Hu Zejun and Li Haizhong:           Classification of Moebius isoparametric hypersurfaces in , Nagoya Mathematical Journal, 179, 147-162, 2005.
 
14.Hu Zejun and Li Haizhong:           A rigidity theorem for hypersurfaces with positive Moebius Ricci curvature in, Tsukuba Journal of Mathematics, 29 (1), 29-47, 2005.
 
15.Hu Zejun and Li Haizhong:           Classification of hypersurfaces with parallel Moebius second fundamental form in ,Science in China Ser. A Mathematics, 47 (3), 1-14, 2004.
 
16.Hu Zejun and Li Haizhong:           Willmore Lagrangian spheres in the complex Euclidean space,Annals of Global Analysis and Geometry, 25 (1), 73-98, 2004.
 
17.Hu Zejun and Li Haizhong:           A new variational characterization of n-dimensional space forms,Transactions of the American Mathematical Society, 356 (8), 3005-3023, 2004.
 
18.Hu Zejun and Li Haizhong:           Scalar curvature, Killing vector fields and harmonic one-forms on compact Riemannian manifolds,Bulletin of the London Mathematical Society, 36 (5), 587-598, 2004.
 
19.Hu Zejun and Li Haizhong:           Willmore submanifolds in a Riemannian manifold,          Proceedings of the Workshop on Contemporary Geometry and Related Topics, pp. 251-275, Published by World Scientific, 2004.
 
20.Hu Zejun and Li Haizhong:           Submanifolds with constant Moebius scalar curvature in S^n, Manuscripta Mathematica, 478 (3), 887-302, 2003.
 
21.Hu Zejun and Wei Guoxin:           On the nonexistence of stable minimal submanifolds and the Lawson-Simons conjecture, Colloquium Mathematicum, 96 (5), 293-224, 2003.
 
22.Hu Zejun and Li Haizhong:           Complete submanifolds with parallel mean curvature and finite total curvature, Geometry and Topology of Submanifolds X, eds. W.H.Chen et al.(pp.53-86), (2000).
 
23.Hu Zejun and Sun Zhenzu:           A new interpretation for the B\"acklund transformation of the Sine-Gordon equation, Kodai Mathematical Journal, 23 (1), 100-104, (2000).
 
24.Hu Zejun:           A Liouville theorem for a class of nonlinear elliptic equations, Acta Mat hematica Scientia, 20 (4), 474-479, 2000. (in Chinese)
 
25.Hu Zejun:           Conformal deformations for prescribing Gaussian curvature on , Chinese Annals of Mathematics, 20 (5), 587-596, (1999). (in Chinese)
 
26.Hu Zejun:           Isometric immersions from the hyperbolic space  into , Colloquium Mathematicum, 79 (1), 17-23, (1999).
 
27.Hu Zejun:           Conformal deformations for prescribing scalar curvature on Riemannian manifolds with negative curvature, Acta Mathematica Sinica, New series, 14 (3), 361-370, (1998).
 
28.Hu Zejun and Zhao Guosong:           Classification of isometric immersions of the hyperbolic space  into , Geometriae Dedicata, 65 (1), 47-57, (1997).
 
29.Hu Zejun and Zhao Guosong:           Isometric immersions from the hyperbolic space  into , Proceedings of the American Mathematical Society, 125 (9), 2693-2697, (1997).
 
30.Hu Zejun and Li Haizhong:           A global pinching theorem for compact surfaces in  with constant mean curvature, Acta Mathematica Sinica, New Series, 12 (2), 126-132, (1996).
 
31.Hu Zejun and Sun Zhenzu:           Submanifolds in space forms with parallel mean curvature vector, Journal of Mathematical Research and Exposition, 16 (1), 69-75, (1996). (in Chinese)
 
32.Hu Zejun:           Complete hypersurfaces with constant mean curvature and nonnegative sectional curvature, Proceedings of the American Mathematical Society, 123 (9), 2835-2840, (1995).
 
33.Zejun Hu andShujie Zhai,CLASSIFICATION OF MOEBIUS ISOPARAMETRIC HYPERSURFACES  IN THE UNIT SIX-SPHERE,           Tohoku Math.J.60 (2008),499-526
 
34.Zejun Hu, Mike Scherfner, Shujie Zhai, On spacelike hypersurfaces with constant scalar curvature in the de Sitter space,           Differential Geometry and its Applications 25 (2007) 594–611
 
35.Zejun Hu andShujie Zhai, Hypersurfaces of the hyperbolic space with constant scalar curvature            Results in Mathematics, 48(2005), 65-88
团队成员主要获奖情况

胡泽军曾获河南省自然科学优秀学术论文奖一等奖2次和二等奖3次,河南省教育厅自然科学优秀学术论文奖一等奖3次和二等奖一次。为河南省优秀中青年骨干教师(1998),河南省跨世纪学术与技术带头人培养对象(1999),河南省优秀教师(2004),郑州大学“三育人”先进个人和“师德标兵”(2005)。

 

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